The improvement of fidelities for two- and multi-qubit quantum gates is a main driver of research in the field of quantum computing: High-fidelity two-qubit gates are essential for the realization of deep quantum circuits in noisy near-term digital quantum devices [1]} as well as for the realization of fully-fledged fault tolerant quantum computers in the long term
 [2]}, [3]}, [4]}, [5]}, while
high-fidelity \(k\) -qubit quantum gates (\(k>2\) ) may drastically reduce the gate count for quantum algorithms and enable fault tolerant quantum computation schemes adapted to specific platforms [6]}, [7]}.
